Quantum SU$(2|1)$ supersymmetric $\mathbb{C}^N$ Smorodinsky--Winternitz system
Abstract
We study quantum properties of SU supersymmetric (deformed , supersymmetric) extension of the superintegrable Smorodinsky--Winternitz system on a complex Euclidian space . The full set of wave functions is constructed and the energy spectrum is calculated. It is shown that SU supersymmetry implies the bosonic and fermionic states to belong to separate energy levels, thus exhibiting the "even-odd" splitting of the spectra. The superextended hidden symmetry operators are also defined and their action on SU multiplets of the wave functions is given. An equivalent description of the same system in terms of superconformal SU quantum mechanics is considered and a new representation of the hidden symmetry generators in terms of the SU ones is found.
Cite
@article{arxiv.2009.14273,
title = {Quantum SU$(2|1)$ supersymmetric $\mathbb{C}^N$ Smorodinsky--Winternitz system},
author = {Evgeny Ivanov and Armen Nersessian and Stepan Sidorov},
journal= {arXiv preprint arXiv:2009.14273},
year = {2022}
}
Comments
1+25 pages, 2 figures, a new affiliation added and Acknowledgments extended; published version